# GPU-Accelerated Forward-Backward algorithm with Application to Lattice-Free MMI

arXiv: https://arxiv.org/abs/2112.00709 · HTML: https://mlsanity.com/paper/2112.00709/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 18 references that are in the map.
- First posted on arXiv 22 Oct 2021.

## Builds on (most cited first, 4 of 4)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Achieving Human Parity in Conversational Speech Recognition](https://mlsanity.com/paper/1610.05256/) (2016)
- [Effective Extensible Programming: Unleashing Julia on GPUs](https://mlsanity.com/paper/1712.03112/) (2017)
- [PyChain: A Fully Parallelized PyTorch Implementation of LF-MMI for End-to-End ASR](https://mlsanity.com/paper/2005.09824/) (2020)

## Built on by (most cited first, 2 of 2)

- [Bregman Conditional Random Fields: Sequence Labeling with Parallelizable Inference Algorithms](https://mlsanity.com/paper/2506.00732/) (2025)
- [Revisiting joint decoding based multi-talker speech recognition with DNN acoustic model](https://mlsanity.com/paper/2111.00009/) (2021)

## Abstract (arXiv)

We propose to express the forward-backward algorithm in terms of operations between sparse matrices in a specific semiring. This new perspective naturally leads to a GPU-friendly algorithm which is easy to implement in Julia or any programming languages with native support of semiring algebra. We use this new implementation to train a TDNN with the LF-MMI objective function and we compare the training time of our system with PyChain - a recently introduced C++/CUDA implementation of the LF-MMI loss. Our implementation is about two times faster while not having to use any approximation such as the "leaky-HMM".